Chapter 2 HW (1-3)

Assignment PDF

1. Definitions and Vocabulary

a)

Term Pair	Difference	Example
Vector vs Scalar	A vector has both magnitude and direction, while a scalar only has magnitude.	Vector: Force (10 N to the right). Scalar: Temperature (25°C).
Coefficient of Static Friction vs Coefficient of Dynamic Friction	Static friction occurs when surfaces are not sliding, while dynamic friction occurs when surfaces slide.	Static: A book at rest on a table. Dynamic: A book being pushed accross a table.
Internal Force vs External Force	Internal forces act within a system, while external forces act on the system from outside.	Internal: Force between molecules in a stretched rubber band. External: Gravity acting on a falling object.
Tensile Force vs Compressive Force	Tensile force pulls objects apart, while compressive force pushes objects together.	Tensile: A rope being pulled from both ends. Compressive: A column supporting a building’s weight.
Resultant Force vs Net Force	The resultant force is the single force that has the same effect as the combination of some other forces. Net force is the sum of all forces acting on an object. Depending on the system being described, these are usually interchangable.	Resultant: Two forces of 5 N and 3 N acting at a 90° angle result in a 5.83 N diagonal force. Net Force: A 10 N force pushing east and a 5 N force pushing west gives a net force of 5 N east.
Weight vs Mass	Weight is the force exerted by gravity on an object, while mass is the amount of matter in the object.	Weight: An object weighing 20 N on Earth. Mass: An object with a mass of 2 kg.

b)

Force
A force is an interaction that causes a change in acceleration. It can be represented as a vector quantity, and is typically measured in newtons (N).

Gravitational Force
In newtonian physics, the gravitational force is an attractive force that pulls bodies of mass towards each other. It is proportional to the mass of the objects and the distance between their centers. The force of gravity on Earth is commonly referred to as weight and is given by the formula $F = mg$, where $m$ is the mass of the object and $g$ is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

Normal Force
The normal force is the force exerted by a surface that supports the weight of or presses into an object. It acts perpendicular (normal) to the surface. For an object resting on a horizontal surface, the normal force opposes the gravitational force on the object, preventing it from accelerating downward.

Frictional Force
Frictional force is the resistive force that opposes sliding between two surfaces in contact. It acts parallel to the surface.

2. Friction

a)

Friction is categorized into three types:

Static friction: When the surfaces are not sliding, $\mu_s$ is used.
Kinetic friction: When the surfaces are sliding, $\mu_k$ is used.

Note: The third type — rolling friction — will not be discussed here.

b)

Frictional force can be modeled as $F_f = \mu N$, where $\mu$ is some coefficient specific to the surfaces, and $N$ is the normal force between the surfaces. When the surfaces are sliding, $\mu_k$ is used. When they are not, $\mu_s$ is used. Under normal conditions, $\mu_s > \mu_k$.

c)

Feature	Friction Characteristics
Material	Common materials include rubber compounds, leather, or synthetic materials like EVA or polyurethane (hesperian, 2024). Different materials have varying friction coefficients as well as deformation, affecting grip depending on ground surface.
Tread Pattern	Depth & Spacing of Grooves: Deeper, closer grooves displace fluids (like water) and provide better grip on loose surfaces. Shape of Lugs: Round lugs may grip hard surfaces better, while angular lugs excel on softer surfaces. This is because on soft ground, lugs deform the surface and interlock with it. More angular lugs will generally deform the ground more effectively, but may also be less durable. Surface Area: Larger contact area also generally increases friction, especially on soft surfaces. This is because the $F_f = \mu N$ model does not account for deformation.
Flexibility	Flexible Soles: Flexible soles conform better to uneven surfaces, improving grip. Rigid Soles: Rigid soles provide more stability, but may be less adaptable.

Chapter 2 HW (1-3)

1. Definitions and Vocabulary

a)

b)

2. Friction

a)

b)

c)

3. Analyzing Forces Acting on Bodies

a)

References